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Validation of saw log and technological wood assortment recovery and reduction predictions based on cut-to-length harvester data

Allar Padari
Allar Padari
 und 
Ahto Kangur
Ahto Kangur
   | 13. Apr. 2024
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Article Category: Research paper
Online veröffentlicht: 13. Apr. 2024
Seitenbereich: 66 - 89
DOI: https://doi.org/10.2478/fsmu-2023-0013
Schlüsselwörter
© 2023 Allar Padari et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

Proportion of damaged trees depending on tree species and age.
Proportion of damaged trees depending on tree species and age.

Figure 2.

Locations of cutting areas.
Locations of cutting areas.

Figure 3.

Log volume reduction (A, C, E and G) and firewood volume increase (B, D, F and H) depending on stand age and site index class (A, B – Scots pine; C, D – Norway spruce; E, F – Birch spp.; G, H – European aspen).
Log volume reduction (A, C, E and G) and firewood volume increase (B, D, F and H) depending on stand age and site index class (A, B – Scots pine; C, D – Norway spruce; E, F – Birch spp.; G, H – European aspen).

Figure 4.

Birch veneer log recovery depending on site index class and stand element age.
Birch veneer log recovery depending on site index class and stand element age.

Figure 5.

Black alder (left) and grey alder (right) firewood increase, and log volume reduction proportion depending on site index class and stand element age.
Black alder (left) and grey alder (right) firewood increase, and log volume reduction proportion depending on site index class and stand element age.

Figure 6.

Distribution of Scots pine assortments calculated by diameter classes according to actual data, the old model and new model.
Distribution of Scots pine assortments calculated by diameter classes according to actual data, the old model and new model.

Figure 7.

Distribution of Norway spruce assortments calculated by diameter classes according to actual data, the old model and new model.
Distribution of Norway spruce assortments calculated by diameter classes according to actual data, the old model and new model.

Figure 8.

Distribution of birch species (silver and downy birch) assortments calculated by diameter classes according to actual data, the old model and new model.
Distribution of birch species (silver and downy birch) assortments calculated by diameter classes according to actual data, the old model and new model.

Figure 9.

Distribution of European aspen assortments calculated by diameter classes according to actual data, the old model and new model.
Distribution of European aspen assortments calculated by diameter classes according to actual data, the old model and new model.

Figure 10.

Distribution of black alder assortments calculated by diameter classes according to actual data, the old model and new model.
Distribution of black alder assortments calculated by diameter classes according to actual data, the old model and new model.

Figure 11.

Distribution of grey alder assortments calculated by diameter classes according to actual data, the old model and new model.
Distribution of grey alder assortments calculated by diameter classes according to actual data, the old model and new model.

Figure 12.

Old and new model prediction comparison residuals for volumes of Scots pine and Norway spruce assortments.
Old and new model prediction comparison residuals for volumes of Scots pine and Norway spruce assortments.

Figure 13.

Old and new model prediction comparison residuals for volumes of silver and downy birch, and European aspen assortments.
Old and new model prediction comparison residuals for volumes of silver and downy birch, and European aspen assortments.

Figure 14.

Old and new model prediction comparison residuals for volumes of black and grey alder assortments.
Old and new model prediction comparison residuals for volumes of black and grey alder assortments.

Figure 15.

Average model residuals by tree species.
Average model residuals by tree species.

Figure 16.

Saw log proportions of the total volume of all roundwood assortments by tree species and sources.
Saw log proportions of the total volume of all roundwood assortments by tree species and sources.

Average model residuals for different models for calculating assortment volumes by tree species.

Tree species Assortment Average model residuals, %
old model new model
Scots pine saw log 6.74 −0.01
firewood −1.33 −0.82
Norway spruce saw log 7.78 2.40
firewood −3.67 −2.55
Birch species saw log 11.83 1.23
firewood 2.21 −0.16
European aspen saw log 0.75 0.42
firewood 22.48 −2.34
Black alder saw log −17.98 −7.84
Grey alder saw log −33.45 −2.99

Saw log proportion reduction.

Tree species Age used in the Estonian model Malinen et al. 2007 Estonian model (Figure 3)
MELA-96 MELA-05 Bucking simulation
Pine 60–100 16.04 24.25 18.17 9–28%
Spruce 60–80 2.35 17.79 6.38 10–29%
Birch 50–70 30.27 29.35 41.46 38–64%

Site index classes and site index H100 relationship.

Site index H100, m Site index class Site index class in calculations
< 11.5 5A 6
11.5…15.5 5 5
15.5…19.5 4 4
19.5…23.5 3 3
23.5…27.5 2 2
27.5…31.5 1 1
> 31.5 1A 0

j.fsmu-2023-0013.tab.008

Relative diameter of a tree in relation to the diameter of a stand element Number of trees, per mille
0.4 11
0.5 34
0.6 59
0.7 96
0.8 131
0.9 154
1.0 154
1.1 132
1.2 96
1.3 64
1.4 35
1.5 18
1.6 10
1.7 4
1.8 2

General data on felled elements included in the analysis. Site index class and site index H100 relationship are described in Table 2.

Tree species No. of elements Age, years Site index class
minimum maximum maximum minimum
Scots pine (Pinus sylvestris L.) 14,013 21 219 1A 5A
Norway spruce (Picea abies (L.) H. Karst.) 3,045 16 177 1A 5
Silver and downy birch (Betula pendula Roth, Betula pubescens Ehrh.) 7,145 22 153 1A 5
European aspen (Populus tremula L.) 1,862 23 140 1A 3
Black alder (Alnus glutinosa (L.) Gaertn.) 679 37 138 1A 4
Grey alder (Alnus incana (L.) Moench) 770 18 75 1A 4
Total 27,514 16 219 1A 5A

Parameters of timber assortments (roundwood) used in the analysis.

Tree species Assortment Top diameter, cm Length, m
minimum step Maximum
Scots pine Log 28–… 3.1 0.3 6.1
Log 23–28 3.1 0.3 6.1
Log 18–23 3.1 0.3 6.1
Log 13–18 3.1 0.3 6.1
Log 10–13 3.1 0.3 6.1
Pulpwood 5 3.0 3.0
Firewood 3 3.0 3.0
Norway spruce Log 25–… 3.1 0.3 6.1
Log 18–25 3.1 0.3 6.1
Log 13–18 3.1 0.3 6.1
Log 10–13 3.1 0.3 6.1
Pulpwood 5 3.0 3.0
Firewood 3 3.0 3.0
Silver and downy birch Log 14–… 3.1 0.3 6.1
Pulpwood 5 3.0 3.0
Firewood 3 3.0 3.0
European aspen Log 14–… 3.1 0.3 6.1
Pulpwood 5 3.0 3.0
Firewood 3 3.0 3.0
Black alder Log 18–… 3.1 0.3 6.1
small log 14–18 3.1 0.3 6.1
Firewood 3 3.0 3.0
Grey alder Log 18–… 3.1 0.3 6.1
small log 14–18 3.1 0.3 6.1
Firewood 3 3.0 3.0

Equation parameters obtained by comparing roundwood assortment volumes.

Tree species Assortment a b c d f i R2 p-value
Scots pine Log volume reduction −0.4560 −6.7947 −46.8016 99 100 1 0.0356 < 0.0001
Firewood increase 2.7817 1.0015 267.0156 99 100 1 0.0233 < 0.0001
Norway spruce Log volume reduction 0.2145 6.7871 −0.0656 1 20 1.1 0.0158 < 0.0001
Firewood increase −3.1086 17.2571 −91.9444 49 50 0.1 0.0195 < 0.0001
Silver and downy birch Log volume reduction 1.0622 9.1595 0.3487 10 50 1 0.0945 < 0.0001
Firewood increase 0.1733 3.2363 0.0063 0,1 1 1 0.0052 < 0.0001
Veneer log −3.6396 10.4272 −2.6481 10 20 0.1 0.1445 < 0.0001
European aspen Log volume reduction 1.0522 12.6587 15.8415 49 50 1 0.1991 < 0.0001
Firewood increase −1.0607 28.4761 −0.0969 0.1 0.2 0.1 0.0381 < 0.0001
Black alder Log volume reduction 0.6106 22.1975 −0.0837 1 2 1 0.0789 < 0.0001
Grey alder Log volume reduction −6.106 12.485 −61.485 90 100 1 0.0353 0.0257

The parameter n of the volume change Equation 3 and the parameters of the Equation for calculating its coefficients a, b and c (Equation 5).

Tree species Formula Constant Equation coefficients
k l m n
Scots pine log volume reduction a −2.259 0.24693 −0.01345 3
b 11.35752 −2.10076 0.1712
c 894.235 −304.766 28.869
firewood increase a −3.3503 0.0159 −0.0013 2
b 1.5375 −0.0271 0.0022
c 1.5328 −0.0261 0.0021
Norway spruce log volume reduction a −0.89371 −0.13886 0.01049 4
b 29.4603 4.36432 −0.33114
c −366800 −228124 −4093
firewood increase a −1.66542 −0.06081 0.0012 4
b 29.59224 0.27817 0.09189
c −115756 −24063 89.533
Silver and downy birch log volume reduction a −0.39607 0.06595 −0.0032 5
b 28.784 −1.088 0.042
c 3829316 885112 80082
firewood increase a −1.67591 0.01012 −0.00097 4
b 25.21899 −0.21777 0.02076
c −211985 7782.9 −749.88
veneer block recovery a −2.7282 −0.2457 −0.0683 4
b 30.281 12.921 −1.639
ln(-c) 12.655 0.8226 0.2254
European aspen log volume reduction a 0.09015 0.01429 −0.00061 4
b 27.49482 −0.06593 −0.01049
c −150369 7285 −387
firewood increase a −1.34789 −0.01386 0.0011 5
b 46.31225 0.04688 −0.00447
c 10507971 920148 −82200
Black alder firewood increase a 0.1209 −0.09111 0.01198 10
b 73.66109 −4.70172 0.78866
c −2.703·1015 −5.258·1015 6.974·1014
Grey alder firewood increase a −0.82187 −0.30129 0.00434 7
b 58.03680 −0.13325 5.87003
c 3.048·1011 −2.887·1011 4.242·1012
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